The advantages of weight-training exercise machines are widely recognized. Conventional weight-training exercise machines may feature single or multiple stations which enable a user to perform one or a variety of exercises for developing and toning different muscle groups. For example, the various stations of such exercise machines may include one or more stations that enable a user to exercise muscles of the arms and upper body using “press,” “shrug,” or “curl” types of movements, and one or more stations for exercising muscles of the legs using “squat,” “press,” or “extension” types of movements. Such weight machines provide the desired muscle training capability in a convenient, safe, and efficient manner. Although prior art exercise apparatus have achieved desirable results, novel apparatus and methods that provide improved versatility would have considerable utility.